Map Projection - Study Notes

Lesson summary

A map projection is the representation of the latitudes and longitudes of the globe on a flat sheet of paper. The network formed is called the graticule. Map projection is a mathematical expression that shows the three-dimensional surface of the earth on a two-dimensional plane, so it distorts one or more map properties such as shape, size, area or direction.

Classification of map projections

Map projections are classified on four criteria:

• Method of construction
• Developable surface used
• Projection properties
• Position of light source

By method of construction

• Perspective projections: made with the help of the shadow cast from an illuminated globe on to a developable surface.
• Non-perspective projections: the developable surface is only assumed to cover the globe; construction uses mathematical calculations.

By developable surface

Types within each surface

• Normal cylindrical (tangent to the equator): Equirectangular, Mercator, Lambert's Cylindrical Equal Area, Gall's Stereographic Cylindrical and Miller cylindrical.
• Transverse cylindrical (tangent to a meridian): Cassini, Transverse Mercator, Transverse cylindrical Equal Area and Modified Transverse Mercator.
• Oblique cylindrical (tangent to another point): only the Oblique Mercator.
• Tangent conical: the cone touches only one parallel (the standard parallel).
• Secant conical: the cone is not big enough to cover the curvature of the earth and intersects it twice, at two parallels.
• Zenithal aspects: equatorial (plane tangent to a point on the equator), oblique (between a pole and the equator) and polar (at one of the poles).

By properties

• Equal area (homolographic): areas of different parts of the earth are correct.
• True shape (orthomorphic): shapes of different parts of the earth are correct.
• True scale (equidistant): no projection keeps correct scale throughout; it can be kept only along some parallels or meridians.

By position of light source

Constructed projections and their properties

Cylindrical Equal Area (Lambert's)

• Devised by J.H. Lambert in 1772; a normal perspective projection on a cylinder tangent at the equator.
• Parallels and meridians are straight lines that meet at right angles.
• Distance between parallels decreases toward the poles; meridians are equally spaced.
• Scale is true along the equator but exaggerated along other parallels.

Cylindrical Equi-distant

• Cylinder tangent to the equator; believed to be invented by Marinus of Tyre about C.E. 100.
• Poles are straight lines equal to the equator; meridians are equally spaced straight lines half as long as the equator.
• Parallels are straight, equally spaced, perpendicular to meridians and equal to the equator.
• Scale is true only along the equator; neither equal area nor orthomorphic, so used for general purposes only.

Polar Zenithal Equal Area (Lambert's Equal Area)

• The pole is the centre; parallels are concentric circles; meridians radiate from the pole with correct angular distance and cut parallels at right angles.
• Scale along parallels increases away from the centre and this is balanced along the meridians, so the projection is equal area.
• Used for political and distribution maps of polar regions and for large areas of the Northern Hemisphere.

Polar Zenithal Equi-distant

• The pole is the centre; parallels are concentric circles drawn at true distances; meridians radiate from the pole.
• Used for maps of polar areas for general purposes.

Construction steps at a glance